What is the Least Common Multiple of 51300 and 51312?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 51300 and 51312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51300 and 51312, than apply into the LCM equation.

GCF(51300,51312) = 12
LCM(51300,51312) = ( 51300 × 51312) / 12
LCM(51300,51312) = 2632305600 / 12
LCM(51300,51312) = 219358800

Least Common Multiple (LCM) of 51300 and 51312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51300 and 51312. First we will calculate the prime factors of 51300 and 51312.

Prime Factorization of 51300

Prime Factorization of 51312

Now multiplying the highest exponent prime factors to calculate the LCM of 51300 and 51312.

LCM(51300,51312) = 2⁴ × 3³ × 5² × 19¹ × 1069¹
LCM(51300,51312) = 219358800